Density dependent behavior at habitat boundaries and the allee effect

Habitat edges can have a number of effects on populations, including modifying their patterns of dispersal. Dispersal patterns can influence population dynamics. In this paper, we explore the possible effects of a pattern of dispersal where the response of organisms to the boundary of a habitat patch depends on their local density. We model a population of organisms diffusing and growing logistically inside a patch, but with the likelihood of an individual crossing the patch boundary to leave the patch decreasing as the local density of conspecifics within the patch increases. Such behavior at patch boundaries has been observed among Glanville fritillary butterflies, and has been proposed as a mechanism for generating an Allee effect at the patch level. Our models predict that the behavior can indeed induce an Allee effect at the patch level even though there is no such effect built into the local population dynamics inside the patch. The models are relatively simple and are not intended to give a complete description of any particular population, but only to verify the idea that the mechanism of density-dependent dispersal behavior at a patch boundary is capable of altering population dynamics within the patch.